Dispersion reactor models pseudo-homogeneous

The units of rv are moles converted/(volume-time), and rv is identical with the rates employed in homogeneous reactor design. Consequently, the design equations developed earlier for homogeneous reactors can be employed in these terms to obtain estimates of fixed bed reactor performance. Two-dimensional, pseudo homogeneous models can also be developed to allow for radial dispersion of mass and energy. 

Equations 12.7.28 and 12.7.29 provide a two-dimensional pseudo homogeneous model of a fixed bed reactor. The one-dimensional model is obtained by omitting the radial dispersion terms in the mass balance equation and replacing the radial heat transfer term by one that accounts for thermal losses through the tube wall. Thus the material balance becomes... 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The conventional two-dimensional pseudo-homogeneous reactor model consists of the continuity equation (11.1) and the simplified momentum equation (11.3) defined in connection with the pseudo-homogeneous dispersion model. The species mass and temperature equations are extended to 2D by adding postulated diffusion terms in the radial space dimension [3]. 

Vanden Bussche and Proment [13] simulated an adiabatic Bench Scale Reactor using a pseudo-homogeneous one-dimensional model. Using a similar pseudo-homogeneous axial dispersion model Jakobsen et al [5] obtained axial concentration and temperature profiles that were hardly distinguishable from the pseudo-homogeneous one-dimensional model results of Vanden Bussche and Proment [13]. 

The use of a full 2D pseudo-homogeneous axi-S3Tnmetric model has the advantage, compared to the conventional 2D pseudo-homogeneous dispersion model, that it enables an evaluation of the influence of a non-uniform void distribution in the reactor. 

The design of such gas-solid catalytic reactors can be approximated by a pseudo-homogeneous model with gas phase in plug flow. In the case of very exothermic reactions accounting for radial dispersion of heat and mass might be useful to prevent excessive particle overheating. The reaction time must find a compromise with the hydrodynamic design, namely the maximum gas velocity and pressure drop. 

Flow of liquids or gases through fixed beds is very important in chemical reaction engineering, since many commercially important processes involve reactors that contain beds of catalyst used to promote a desired reaction. The axial dispersion model has been used extensively to model these flows, even though two phases, fluid and solid, are present. Such a pseudo-homogeneous model assumes the same form we have described in the preceding section if the Peclet number is based on particle dimension and the interstitial fluid velocity is used. In this event... 

In order to minimize the experimental error, special probes were used 25 miniature thermocouples located at 9 different radial positions introduced in an asbesteous honeycomp in a single cross-section of a 50 mm diameter column or 6 capillaries for concentration sampling at 6 radial positions. The large amount of simultaneously obtained data was recorded automatically on a data storage device and subsequently processed with the help of the computer program FIBSAS /19/ for a two-dimensional pseudo-homogeneous dispersion model of a fixed-bed reactor. 

Widespread use of pseudo homogeneous models makes it important to examine the sources of errors involved in the use of these assumptions. This detailed discussion is also necessary when the model is used in a less simplified form, because it gives the degree of confidence of the reactor operation in a quantitative manner. The phenomena causing departure from the pseudo homogeneous model are 1) end effects 2) axial dispersion ... 

For each region a mean value of the void fraction was calculated and a hydraulic radius was defined which was used in a pressure drop correlation. Martin [20] divided the bed into two regions a wall and a bulk region. He calculated for both different flow rates and a different rate of heat transfer. Carbonell [2] also used a two zone model for his analysis of the dispersion phenomena. In more recent work Vortmeyer et al. [5>6] tried to use the complete radial void fraction profile, and so did Chang [3]. They followed the same itinerary outlined by Lerou and Froment [l] and Marivoet et al. [2l]. Starting from the void fraction profile the radial velocity profile is calculated. With both profiles the effective thermal conductivity is established and the temperature and concentration profiles can be calculated by means of a two dimensional pseudo homogeneous model for the reactor. 

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